Unequalizer Skill Level Rating System
A Reverse Engineering Study in Statistical Ratings
By: Aaron DeRenard
A Brief
Thank You:
It is with
my sincerest thanks to the doctorate curriculum master mathematicians that volunteered
their time to tackle this 12+ year endeavor.
I have dedicated a large portion of my life to this project, and I would
never have seen this solved without your hard work. Thanks to you, impassioned league players
everywhere have a chance to understand the integrity of the systems, and robustness
of those systems, that make their experience in this program unique.
How this
system came to be:
In 2010 a
friend of mine convinced me to break the reclusive cycle and come to a pool hall.
That day I met with someone who convinced me to give pool leagues a try. It was at that moment my life took a turn and
this significant project germinated. I
was a 3 starting out. I couldn’t make 2
balls in a row. The players I played with
wanted my game to improve but didn’t want my skill level to improve in the
rating system. They thought they had it
all worked out how to manipulate things.
I would play many matches, and for the most part adjustments took place
as expected. But, from time to time, unforeseen
adjustments would happen and wreck our hopes and dreams of manipulating the
system. It was at that time I knew it
was up to me to be the world beater 3, and the magician behind the curtain who
controlled what happened in the system.
The only way that could happen was through fully understanding the
system. There’s just one problem- the system
was a closely guarded secret.
I was and
still am a lifelong software engineer. I
knew if I could get in the door working with the keepers of the system I would
have the keys to the kingdom. It had to
happen, somehow, and I made it my mission.
I made every
effort to get hired on. I just couldn’t
seem to convince them they needed me. But
there had to be a way. In 2012 I picked
up a book by Kevin Mitnick, a world-renowned cyber security consultant. It was then the plan was born.
In 2012 I
entered the national office and explained I was there on behalf of the
mainframe support vendor as a support engineer and had an appointment for
mandatory security updates. They
questioned my story, didn’t have any scheduled appointments of my coming, but
was also concerned that by turning me away their information security was at
risk. She allowed me to enter their
network operations center with an escort.
That was all I needed. We made
our way to the mainframe and while shutting it down I managed to attach a dirty
USB drive. This drive had code that automatically
installed a scheduled task that analyzed the system for the most
commonly changed data which I suspected would be the rating system
data. That data was periodically copied
and uploaded to a remote server. For 6
months that process ran and collected data until a system update was performed
and it no longer worked. During those 6
months though I collected critical data that painted a picture of statistical trends.
12 years later,
in 2024, during the revolution of artificial intelligence and lexical analytics
the tools to decipher the data, in conjunction with the brilliant minds of mathematicians
and statisticians, the secret algorithm has finally been approximated to a
reasonable degree to reproduce the outcomes of individual matches.
This is my
work, and I openly contribute this work to you.
With this knowledge comes great power.
I trust that you will use it for good, and not abuse it, for the risk is
great the algorithm gets changed to thwart abuse. Be wise, but be in
control.
Components
of the Rating System:
- Skill Levels:
- Each player has a skill level ranging
from 2.0 to 7.99.
- This skill level is the core rating,
and it adjusts after each match.
- Match Outcome:
- A match result is either a win or a
loss.
- The result will affect the skill rating
of both players involved.
- Rating Adjustment Weight:
- For each match (up to 32,767 matches),
the adjustment weight is drawn at random from a bell curve (normal
distribution) of values ranging from -1.0 to 1.0.
- This random weight influences how much
a player's skill rating changes after a match.
- Skill Differential Influence:
- The difference in skill levels between
two opponents influences the size of the rating adjustment.
- If the weaker player wins, their rating
increases more significantly, while the stronger player’s rating
decreases more.
- If the stronger player wins, the
adjustment is less pronounced.
Formula to
Calculate Rating Change:
The formula
for the rating change could be:
Where:
= Change in rating
= Random weight value (from bell curve,
range -1.0 to 1.0)
= Opponent's skill level
= Player's skill level
= +1 for a win, -1 for a loss
Example
Scenarios:
- Example 1:
- Player A Skill Level: 5.5
- Player B Skill Level: 6.2
- Outcome: Player A wins
- Random Weight (W): 0.35
New Skill
Levels:
- Player A: 5.745
- Player B: 6.2 (No change)
- Example 2:
- Player A Skill Level: 7.0
- Player B Skill Level: 4.5
- Outcome: Player B wins
- Random Weight (W): -0.6
New Skill
Levels:
- Player A: 7.0 (No change)
- Player B: 3.0
- Example 3:
- Player A Skill Level: 3.8
- Player B Skill Level: 3.9
- Outcome: Player A wins
- Random Weight (W): 0.75
New Skill
Levels:
- Player A: 3.875
- Player B: 3.9 (No change)
Summary of
the System:
- Randomness: Introduced by the weight
, so no match result is
entirely predictable. - Influence of Skill Differential: Larger differences in skill levels
result in more significant rating adjustments.
- Outcome-Based: Winning always tends to increase skill,
while losing does the opposite, but the magnitude varies based on the
factors mentioned above.